Lutasin ang (2/3)^{-4}*(2/3)^{-3}*(-3/2)^-5+8[(2-1/4)frac{1}{7}-frac{3}{4}]+[(-frac{3}{2})^2*(frac{1}{3})^2]^-1

$$( \frac { 2 } { 3 } ) ^ { - 4 } \cdot ( \frac { 2 } { 3 } ) ^ { - 3 } \cdot ( - \frac { 3 } { 2 } ) ^ { - 5 } + 8 [ ( 2 - \frac { 1 } { 4 } ) \frac { 1 } { 7 } - \frac { 3 } { 4 } ] + [ ( - \frac { 3 } { 2 } ) ^ { 2 } \cdot ( \frac { 1 } { 3 } ) ^ { 2 } ] ^ { - 1 }$$

I-evaluate

$$-\frac{9}{4}=-2.25$$

Mga Hakbang ng Solution

Para mag-multiply ng mga power na may parehong base, i-add ang mga exponent ng mga ito. I-add ang -4 at -3 para makuha ang -7.

$$\left(\frac{2}{3}\right)^{-7}\left(-\frac{3}{2}\right)^{-5}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Kalkulahin ang \frac{2}{3} sa power ng -7 at kunin ang \frac{2187}{128}.

$$\frac{2187}{128}\left(-\frac{3}{2}\right)^{-5}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Kalkulahin ang -\frac{3}{2} sa power ng -5 at kunin ang -\frac{32}{243}.

$$\frac{2187}{128}\left(-\frac{32}{243}\right)+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

I-multiply ang \frac{2187}{128} at -\frac{32}{243} para makuha ang -\frac{9}{4}.

$$-\frac{9}{4}+8\left(\left(2-\frac{1}{4}\right)\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

I-subtract ang \frac{1}{4} mula sa 2 para makuha ang \frac{7}{4}.

$$-\frac{9}{4}+8\left(\frac{7}{4}\times \frac{1}{7}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

I-multiply ang \frac{7}{4} at \frac{1}{7} para makuha ang \frac{1}{4}.

$$-\frac{9}{4}+8\left(\frac{1}{4}-\frac{3}{4}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

I-subtract ang \frac{3}{4} mula sa \frac{1}{4} para makuha ang -\frac{1}{2}.

$$-\frac{9}{4}+8\left(-\frac{1}{2}\right)+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

I-multiply ang 8 at -\frac{1}{2} para makuha ang -4.

$$-\frac{9}{4}-4+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

I-subtract ang 4 mula sa -\frac{9}{4} para makuha ang -\frac{25}{4}.

$$-\frac{25}{4}+\left(\left(-\frac{3}{2}\right)^{2}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Kalkulahin ang -\frac{3}{2} sa power ng 2 at kunin ang \frac{9}{4}.

$$-\frac{25}{4}+\left(\frac{9}{4}\times \left(\frac{1}{3}\right)^{2}\right)^{-1}$$

Kalkulahin ang \frac{1}{3} sa power ng 2 at kunin ang \frac{1}{9}.

$$-\frac{25}{4}+\left(\frac{9}{4}\times \frac{1}{9}\right)^{-1}$$

I-multiply ang \frac{9}{4} at \frac{1}{9} para makuha ang \frac{1}{4}.

$$-\frac{25}{4}+\left(\frac{1}{4}\right)^{-1}$$

Kalkulahin ang \frac{1}{4} sa power ng -1 at kunin ang 4.

$$-\frac{25}{4}+4$$

Idagdag ang -\frac{25}{4} at 4 para makuha ang -\frac{9}{4}.

$$-\frac{9}{4}$$

I-factor

$$-\frac{9}{4} = -2\frac{1}{4} = -2.25$$